We study X-ray tomograqphic reconstruction using statistical methods. The problem is expressed in cylindrical coordinates, which yield significant computatio...

Stochastic Dynamic Programming (SDP) is a powerful approach applicable to nonconvex and stochastic stagewise problems. We investigate the impact of the form...

We propose an iterative method named LSLQ for solving linear least-squares problems \(A x \approx b\) of any shape. The method is based on the Golub and K...

For positive definite linear systems (or semidefinite consistent systems), we use Gauss-Radau quadrature to obtain a cheaply computable upper bound on the ...

NLP.py is a programming environment to model continuous optimization problems and to design computational methods in the high-level and powerful Python l...

We describe a collection of linear systems generated during the iterations of an interior-point method for convex quadratic optimization. As the iteration...

Adaptative cubic regularization (ARC) methods for unconstrained optimization compute steps from linear systems with a shifted Hessian in the spirit of the mo...

In many large engineering design problems, it is not computationally feasible or realistic to store Jacobians or Hessians explicitly. Matrix-free implementat...

A preconditioned variant of the Golub and Kahan (1965) bidiagonalization process recently proposed by Arioli (2013) and Arioli and Orban (2013) allows us to ...

We propose a generalization of the limited-memory Cholesky factorization of Lin and Moré (1999) to the symmetric indefinite case with special interest in sym...

Symmetric quasi-definite systems may be interpreted as regularized linear least-squares problem in appropriate metrics and arise from applications such as re...

We describe the most recent evolution of our constrained and unconstrained testing environment and its accompanying SIF decoder. Code-named SIFDecode and CU...

Projected Krylov methods are full-space formulations of Krylov methods that take place in a nullspace. Provided projections into the nullspace can be compute...

Interior-point methods feature prominently among numerical methods for inequality-constrained optimization problems, and involve the need to solve a sequ...

Interior-point methods in semi-definite programming (SDP) require the solution of a sequence of linear systems which are used to derive the search directions...

OPAL is a general-purpose system for modeling and solving algorithm optimization problems. OPAL takes an algorithm as input, and as output it suggests para...

Implementations of the Simplex method differ only in very specific aspects such as the pivot rule. Similarly, most relaxation methods for mixed-integer ...

The analytic center cutting plane method and its proximal variant are well known techniques for solving convex programming problems. We propose two seq...

We consider a class of infeasible, path-following methods for convex quadratric programming. Our methods are designed to be effective for solving both nonde...

We propose an interior-point algorithm based on an elastic formulation of the \(\ell_1\)-penalty merit function for mathematical programs with complementar...